Both sides were knocked out at the group stage of last season's competition, so they will be hoping to improve on that this time around.
Match preview
Indeed, two points from six matches was not Sturm Graz's ideal return to a European group stage for the first time in a decade, but the Austrians were handed an incredibly tough draw having been placed alongside Monaco, Real Sociedad and PSV Eindhoven.
This time around, they have been drawn against Lazio, Feyenoord and their forthcoming opponents Midtjylland, so they may feel they have an improved chance of finishing third at the very least, which would see them drop into the Europa Conference League.
As such, Thursday's home match against the Danes becomes one of the utmost importance, as realistically it is one which they must be taking three points from if they are to have a realistic shot at progressing from Group F.
Having finished second in the Austrian Bundesliga last season - their best league finish for four seasons - Christian Ilzer will feel confident of improving on last season's European showing, having made a decent enough start domestically with 12 points from seven matches seeing them occupy third position.
Midtjylland, on the other hand, have seriously struggled to get going in the early weeks of the current campaign, taking only nine points from eight matches to lie in eighth position in the Danish Superliga.
Having finished in the top three in 10 of the previous 11 seasons, with Brentford owner Matthew Benham massively improving their fortunes since becoming the club's majority shareholder in July 2014, it has been an alarming couple of months for The Wolves, culminating in former Barcelona B boss Albert Capellas replacing Bo Henriksen in the dugout.
Capellas won his first game in charge away to Brondby last weekend, before losing 2-0 at home to AaB last time out. With a fourth league title in the club's history looking unlikely even at this early stage of the season, the Spaniard may prioritise the Europa League, as he aims to take Midtjylland beyond the group stage for only the second ever time.
A win in Austria on Thursday could significantly galvanise a squad which is clearly lacking morale at present, and provide belief that they could upset the apple cart by finishing ahead of either Lazio or Feyenoord to progress to the knockout rounds.
Sturm Graz form (all competitions):
FC Midtjylland form (all competitions):
Team News
Jorg Siebenhandl, who is Sturm Graz's first-choice goalkeeper, has suffered a minor muscle strain and is facing a race against time to prove his fitness for the visit of Midtjylland on Thursday.
Should he lose that battle, Tobias Schutzenauer will replace him having started in the Austrian Cup recently, while Jakob Jantscher, Otar Kiteishvili and Niklas Geyrhofer are all definitely ruled out through injury.
Midtjylland, meanwhile, will travel without Junior Brumado due to a strained knee, while Pablo Ortiz is doubtful due to a foot injury.
Former Brentford defender Henrik Dalsgaard could come into the team at right-back.
Sturm Graz possible starting lineup:
Schutzenauer; Gazibegovic, Wuthrich, Borkovic, Dante; Hierlander, Stankovic, Prass; Horvat; Boving, Emegha
FC Midtjylland possible starting lineup:
Lossl; Dalsgaard, Sviatchenko, Juninho, Paulinho; Dreyer, Olsson, Evander; Isaksen, Kaba, Sisto
We say: Sturm Graz 1-2 FC Midtjylland
Neither side head into this fixture in the best of form, but the visitors do possess more individual quality and this could be the match which kick-starts Capellas's reign.
The hosts gained only two points from six games in last season's Europa League, so they may be lacking belief that they can compete at this level.